Title: Expanders: From Graphs to Complexes
Speaker: Bharatram Rangarajan (Hebrew University, Jerusalem, Israel)
Date: 26 September 2018
Time: 3 pm
Venue: LH-1, Mathematics Department

The aim of this talk is to give a high-level overview of the theory of expander graphs and introduce motivations and possible approaches to generalizing it to higher dimensions. I shall begin with three perspectives on expansion in graphs- discrepancy, isoperimetry and mixing time, and show a qualitative equivalence of these notions in defining expansion for graphs. Next I shall briefly discuss upper and lower bounds on expansion, and sketch the Lubotzky-Phillips-Sarnak construction of Ramanujan graphs. Finally, I hope to motivate high-dimensional expanders using two interesting topics- the overlapping problem, and the threshold problem.


Contact: +91 (80) 2293 2711, +91 (80) 2293 2265
E-mail: chairman.math[at]iisc[dot]ac[dot]in